add some doctests to algos in backtracking (#11911)

* add some doctests to algos in backtracking

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: 3 people

backtracking/generate_parentheses.py

@@ -64,6 +64,10 @@ def generate_parenthesis(n: int) -> list[str]:
     Example 2:
     >>> generate_parenthesis(1)
     ['()']
+
+    Example 3:
+    >>> generate_parenthesis(0)
+    ['']
     """
 
     result: list[str] = []

backtracking/n_queens.py

@@ -33,6 +33,14 @@ def is_safe(board: list[list[int]], row: int, column: int) -> bool:
     False
     >>> is_safe([[0, 0, 1], [0, 0, 0], [0, 0, 0]], 1, 1)
     False
+    >>> is_safe([[1, 0, 0], [0, 0, 0], [0, 0, 0]], 1, 2)
+    True
+    >>> is_safe([[1, 0, 0], [0, 0, 0], [0, 0, 0]], 2, 1)
+    True
+    >>> is_safe([[0, 0, 0], [1, 0, 0], [0, 0, 0]], 0, 2)
+    True
+    >>> is_safe([[0, 0, 0], [1, 0, 0], [0, 0, 0]], 2, 2)
+    True
     """
 
     n = len(board)  # Size of the board

backtracking/word_break.py

@@ -66,6 +66,9 @@ def word_break(input_string: str, word_dict: set[str]) -> bool:
 
     >>> word_break("catsandog", {"cats", "dog", "sand", "and", "cat"})
     False
+
+    >>> word_break("applepenapple", {})
+    False
     """
 
     return backtrack(input_string, word_dict, 0)